Particle Fluctuations in Mesoscopic Bose Systems
Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose−Einstein condensation temperature <inline-formula> <math display="inline">...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/5/603 |
| _version_ | 1798006497493385216 |
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| author | Vyacheslav I. Yukalov |
| author_facet | Vyacheslav I. Yukalov |
| author_sort | Vyacheslav I. Yukalov |
| collection | DOAJ |
| description | Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose−Einstein condensation temperature <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>, as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality <i>d</i> and on the confining dimension <i>D</i> of the system. The consideration shows that mesoscopic systems, experiencing Bose−Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> above <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> and in a box of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>4</mn> </mrow> </semantics> </math> </inline-formula> below <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> above <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> and of a confining dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>></mo> <mn>4</mn> </mrow> </semantics> </math> </inline-formula> below <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>; (iii) the interacting Bose system is confined in a rectangular box of dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> above <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>, while below <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>, particle interactions stabilize the Bose-condensed system, making it stable for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula>; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions. |
| first_indexed | 2024-04-11T12:55:50Z |
| format | Article |
| id | doaj.art-29702c20293f493886670eeff39fe253 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T12:55:50Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-29702c20293f493886670eeff39fe2532022-12-22T04:23:04ZengMDPI AGSymmetry2073-89942019-05-0111560310.3390/sym11050603sym11050603Particle Fluctuations in Mesoscopic Bose SystemsVyacheslav I. Yukalov0Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, RussiaParticle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose−Einstein condensation temperature <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>, as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality <i>d</i> and on the confining dimension <i>D</i> of the system. The consideration shows that mesoscopic systems, experiencing Bose−Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> above <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> and in a box of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>4</mn> </mrow> </semantics> </math> </inline-formula> below <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> above <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> and of a confining dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>></mo> <mn>4</mn> </mrow> </semantics> </math> </inline-formula> below <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>; (iii) the interacting Bose system is confined in a rectangular box of dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> above <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>, while below <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>, particle interactions stabilize the Bose-condensed system, making it stable for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula>; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.https://www.mdpi.com/2073-8994/11/5/603Bose systemsasymptotic symmetry breakingBose–Einstein condensationparticle fluctuationsstability of Bose systems |
| spellingShingle | Vyacheslav I. Yukalov Particle Fluctuations in Mesoscopic Bose Systems Symmetry Bose systems asymptotic symmetry breaking Bose–Einstein condensation particle fluctuations stability of Bose systems |
| title | Particle Fluctuations in Mesoscopic Bose Systems |
| title_full | Particle Fluctuations in Mesoscopic Bose Systems |
| title_fullStr | Particle Fluctuations in Mesoscopic Bose Systems |
| title_full_unstemmed | Particle Fluctuations in Mesoscopic Bose Systems |
| title_short | Particle Fluctuations in Mesoscopic Bose Systems |
| title_sort | particle fluctuations in mesoscopic bose systems |
| topic | Bose systems asymptotic symmetry breaking Bose–Einstein condensation particle fluctuations stability of Bose systems |
| url | https://www.mdpi.com/2073-8994/11/5/603 |
| work_keys_str_mv | AT vyacheslaviyukalov particlefluctuationsinmesoscopicbosesystems |